The Orthodox, Copts and Protestants have their own reasoning on the matter.

As do the Arians concerning the divinity of Christ.

Are there any Arians around? Arianism flatly contradicts Scripture and the most basic and fundamental Christian belief.

The non-Catholic Christians still exist in very significant numbers and interpret those scriptural passages used in support of the Petrine primacy differently than Roman Catholicism does. Some Fathers also did so, there's certainly precedence in scriptural exegesis. It's not a clear and cut thing that non-Catholics don't accept out of mere pride or obstinacy. It's a bit disingenuous to constantly portray them as dishonest or stupid. Even an honest Catholic apologist has to admit that Petrine primacy, not to mention supremacy, was not very conspicious during the first millennia of Christendom. It's one of those dogmas that became "explicit" and "defined" more than one thousand years after the fact.